Background Simultaneous Linear Equations

Multiple-Choice Test

Chapter 04.01 Background Simultaneous Linear Equations

6 2 3 9 0 1 2 3 1. Given A =   then A is a (an) ______matrix. 0 0 4 5   0 0 0 6

(A) diagonal (B) identity (C) lower triangular (D) upper triangular

2. A square matrix A is lower triangular if

(A) aij  0, j  i

(B) aij  0, i  j

(C) aij  0, i  j

(D) aij  0, j  i

3. Given 12.3  12.3 20.3   2 4      [A]  11.3  10.3 11.3 , [B]   5 6  10.3  11.3 12.3 11  20

then if C  AB, then

c31  ______

(A)  58.2 (B)  37.6 (C) 219.4 (D) 259.4

04.01.1 04.01.2 Chapter 04.01

4. The following system of equations has ______solution(s). x  y  2 6x  6y  12 (A) infinite (B) no (C) two (D) unique

5. Consider there are only two computer companies in a country. The companies are named Dude and Imac. Each year, Dude keeps 1/5th of its customers, while the rest switch to Imac. Each year, Imac keeps 1/3rd of its customers, while the rest switch to Dude. If in 2003, Dude had 1/6th of the market and Imac had 5/6th of the market, what will be the share of Dude computers when the market becomes stable? (A) 37/90 (B) 5/11 (C) 6/11 (D) 53/90

6. Three kids - Jim, Corey and David receive an inheritance of $2,253,453. The money is put in three trusts but is not divided equally to begin with. Corey's trust is three times that of David's because Corey made an A in Dr. Kaw’s class. Each trust is put in an interest generating investment. The three trusts of Jim, Corey and David pays an interest of 6%, 8%, 11%, respectively. The total interest of all the three trusts combined at the end of the first year is $190,740.57. The equations to find the trust money of Jim ( J ), Corey (C ) and David ( D ) in a matrix form is  1 1 1  J   2,253,453       (E)  0 3 1 C   0  0.06 0.08 0.11D 190,740.57  1 1 1  J   2,253,453       (F)  0 1  3 C   0  0.06 0.08 0.11D 190,740.57 1 1 1  J   2,253,453       (G) 0 1  3C   0  6 8 11 D 190,740.57 1 1 1  J   2,253,453       (H) 0 3 1C   0  6 8 11D 19,074,057

For a complete solution, refer to the links at the end of the book.

04.01.2